Histograms

Responding to a tweet from Dani Quinn:

My preferred introduction would be to show the following frequency table, and subsequently ask students to represent this information in a diagram.

Age Frequency
5 ≤ age < 15 10
15 ≤ age < 20 10
20 ≤ age < 30 10
30 ≤ age < 60 10

Specifically, the frequencies are equal, while the class widths vary.

Students develop an understanding of the limitations of a frequency diagram, and we have a gradual discussion, using the following as a guide:

Histograms have a number of uses relating to visually indicating the distribution of the data (e.g. skewnewss). However, they are not the best tool for other tasks (e.g. identifying frequencies).

Students have rarely (conciously) encountered them at the point that they are first introduced in the classroom, and often struggle to underhstand their purpose.

To me, it is very much one of Dan Meyer’s:

If [x] is aspirin, then how do I create the headache?

With histograms being the [x] to the headache that is an appropriate visual representation of the frequency table.